Cooperative interactions in the binding of multiple signaling molecules is a common mechanism for enhancing the sensitivity of biological signaling systems. It is widely assumed this increase in sensitivity of the mean response implies the ability to detect smaller signals. Extending the classic work of Berg and Purcell [Biophys. J. 20, 193 (1977)] on the physical limits of chemoreception, we show that the random arrival of diffusing signaling molecules at receptor sites constitutes a noise source that is not reduced by cooperativity. Cooperativity makes reaching this limit easier, but cannot reduce the limit itself.